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2014 Simple and High-Accurate Schemes for Hyperbolic Conservation Laws
Renzhong Feng, Zheng Wang
J. Appl. Math. 2014: 1-13 (2014). DOI: 10.1155/2014/275425


The paper constructs a class of simple high-accurate schemes (SHA schemes) with third order approximation accuracy in both space and time to solve linear hyperbolic equations, using linear data reconstruction and Lax-Wendroff scheme. The schemes can be made even fourth order accurate with special choice of parameter. In order to avoid spurious oscillations in the vicinity of strong gradients, we make the SHA schemes total variation diminishing ones (TVD schemes for short) by setting flux limiter in their numerical fluxes and then extend these schemes to solve nonlinear Burgers’ equation and Euler equations. The numerical examples show that these schemes give high order of accuracy and high resolution results. The advantages of these schemes are their simplicity and high order of accuracy.


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Renzhong Feng. Zheng Wang. "Simple and High-Accurate Schemes for Hyperbolic Conservation Laws." J. Appl. Math. 2014 1 - 13, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010585
MathSciNet: MR3178956
Digital Object Identifier: 10.1155/2014/275425

Rights: Copyright © 2014 Hindawi


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